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Our goal is twofold: (i) to analyze the role of the order of the fractional derivative,<jats:italic>\u03b1<\/jats:italic>, on the efficacy of the immune response, (ii) to examine the immune response for distinct transmission functions, in the presence of saturated CTL response. We compute the reproduction number of the model and state the stability of the disease-free equilibrium. We discuss the results of the model from an epidemiological point of view.<\/jats:p>","DOI":"10.1051\/mmnp\/2019007","type":"journal-article","created":{"date-parts":[[2019,3,26]],"date-time":"2019-03-26T08:57:27Z","timestamp":1553590647000},"page":"307","source":"Crossref","is-referenced-by-count":14,"title":["Immune response in HIV epidemics for distinct transmission rates and for saturated CTL response"],"prefix":"10.1051","volume":"14","author":[{"given":"Ana R.M.","family":"Carvalho","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0729-1133","authenticated-orcid":false,"given":"Carla M.A.","family":"Pinto","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2019,3,26]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13662-016-1057-2","volume":"2017","author":"Ammi","year":"2017","journal-title":"Adv. Differ. 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